LINEAR BISPECTRUM OF SIGNALS AND IDENTIFICATION OF NONMINIMUM PHASE FIR SYSTEMS DRIVEN BY COLORED INPUT

We address the identification of nonminimum phase finite impulse response (FIR) systems driven by third-order stationary, colored signals that are not linear processes. First, we discuss modeling the linear part of the bispectrum of a signal, called the "linear bispectrum." We decompose the bispectrum of a signal into two multiplicative factors. The linear bispectrum is defined as the factor of the bispectrum that can exactly be modeled using a third-order white noise driven linear shift-invariant (LSI) system. We show that the desired Fourier-phase and -magnitude information about the unknown LSI system is contained in the linear bispectrum of the system output. Thus, we propose representing the linear bispectrum of the output of the unknown LSI system using an ARMA model, where the MA parameters correspond to the unknown FIR system impulse response coefficients, and the AR parameters model the linear bispectrum of the input signal. We then provide an algorithm to identify the MA and AR parameters of this ARMA model. Finally, we elaborate on how the proposed method is different from fitting an ARMA model directly to the bicumulants or the bispectrum of the system output. Application of the proposed method to blur identification is presented.